6) Calculate the volume and surface area of the cuboid below:
Volume =
Surface area =

Solution

Step 1

Write out the expression for the probability of an event occurring

For this question,

The number of required events = The number of students that are male and Junior= 2

The total number of events = The total number of male students= 4+6+2+2 = 14

Step 2

Find the required probability after substitution

Hence the probability the student is a junior given its a male = 1/7

In percentage, the probability will be

Where x is the required percentage, to the nearest whole percent, the final answer is 14%

The height of the actual building, given the height of the model, can be found to be 1, 455 feet

The model is such that every inch of the building on the model is 75 feet of the actual building.

This means that if the height of the building in the model is 19 ² / ₅ inches, then the height of the actual building would be:

= Height of building in model x Scale factor per inch

= 19 ² / ₅  x 75

= 97 / 5 x 75

= 1, 455 feet

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Apply the trigonometric functions:

Sin B = opposite side / hypotenuse:

Where:

B : angle

Opposite sid

Answer:

17.1

Step-by-step explanation:

Exponential Functions:

y=ab^x

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r=1−0.064=0.936

Write Exponential Function:

y=310(0.936)^x

Put it all together

Plug in y-value:

100=310(0.936)^x

100/310 = 310(0.936)^x/310

​

Divide both sides by 310

0.322581=0.936^x

\log 0.322581=\log 0.936^x

Take the log of both sides

log0.322581=xlog0.936

Use power rule to bring x to the front

log0.322581/log0.936 = xlog0.936/log0.936

​

Divide both sides by log(0.936)

17.106221=x

x≈17.1

17.12 will it take until there are 100 grams of the element remaining

Two or more expressions with an Equal sign is called as Equation.

Given that  element with a mass of 310 grams decays by 6.4% per minute.

we need to find the time will it be until there are 100 grams of the element remaining

y=abˣ

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r

=1−0.064

=0.936

Plug in these values in the formula

y=310(0.936)ˣ

100=310(0.936)ˣ

Divide both sides by 310

100/310 = (0.936)ˣ

0.322581=0.936ˣ

Apply log on both sides

log 0.322581=xlog0.936

Divide both sides by log0.936

log0.322581/log0.936 = xlog0.936/log0.936

17.106221=x

Hence, 17.12 will it take until there are 100 grams of the element remaining

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Answer:

2^25/2

Step-by-step explanation:

We express them as a power of 2 using laws of indices

The value of [tex]a^{2} +\frac{1}{a^{2} }[/tex] if  [tex]a=\frac{2+\sqrt{5} }{2}[/tex] is solved to be

The equation is solved by substituting for a in the given equation [tex]a^{2} +\frac{1}{a^{2} }[/tex]

[tex]a^{2} +\frac{1}{a^{2} }[/tex]

substituting for a

[tex](\frac{2+\sqrt{5} }{2})=(1+\frac{\sqrt{5} }{2})[/tex]

[tex](1+\frac{\sqrt{5} }{2})^{2} =(1+\frac{\sqrt{5} }{2})*(1+\frac{\sqrt{5} }{2})=1+2\frac{\sqrt{5} }{2} +\frac{5}{4}=\sqrt{5} +\frac{9}{4}=4.48607[/tex]

= 4.8607 + 1/4.48607

= 5.0664

Substituting the value of a in the equation and solving resulted to 5.1

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Answer: 3.86587352821

Step-by-step explanation: This cannot be solved by hand, you need a calculator for this!

Answer:

y=3x-11

Step-by-step explanation:

In this question, we will use the point slope form:

Which has the equation:

[tex]y-y_1=m(x-x_1)\\subsitute:\\y+5 = 3(x-2) , (y--5=+5)\\y+5=3x-6\\y=3x-11[/tex]

Hope this helps!

The parent quadratic function is 2 unit right and 3 units up.

Given function is

f(x) = (x-2)² +3

= x² - 2² - 2×x×2 + 3

= x2 - 4 - 4X + 3

= X² - 4X -1

Parent function g(x) = x²

The parent function is shifted to 2 units in right and 3 units up.

Parent function transformations are shown in blue. This is a 1 unit shift down. Mirroring of the x-axis is done functionally by multiplying the superordinate function by the negative function.

A parent function is the simplest function that satisfies the definition of a particular function type. For example, consider linear functions that form a family of functions.

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Disclaimer:- your question is incomplete, Please see below for the complete question.

Which phrase best describes the transformation(s) of the following graph from the parent quadratic function? f(x)=(x-2)^2+3

Answer:

11.10 or 11.1

Step-by-step explanation:

1. 15 x 0.075= 1.125 or 1.13

2. 15-1.13=13.87

3. 13.87 x 0.20= 2.774 or 2.77

4. 13.87 -  2.77 = 11.10 or 11.1

Recall the definition of the sine of an angle on a right triangle:

On the other hand, according to this diagram, the values for tan(A) and cos(A) are given by:

Since 180≤A≤270, the right triangle that corresponds to the angle A on the coordinate plane looks as follows:

Where a and b are negative distances.

Since sin(A)=-4/7, we can assume that a=-4 and c=7. Use the Pythagorean Theorem to find the exact value of b:

We know that b should be negative. Then:

Substitute b=-sqrt(33) and c=7 to find the exact values for cos(A) and tan(A):

Therefore, the exact values for cos(A) and tan(A) are:

year's

this year´s profit is $ 472857

Explanation

we can easily solve this by using a rule of three

so

Step 1

a)let x represents this year's profit

so

if it is decreases by 2.1 %

so, this year's profit is 97.9% of the last year profit

hence

we can make a proportion

finally, solve for x,

therefore

this year´s profit is $ 472857

I hope this helps you

The slope of the given situation of selling breakfast platters is 0.90.

Given, the platter of 12 bagels costs $10.80.

The extra cost of $6.50 for a gallon of coffee.

To find the slope of the situation, we convert the situation into the equation of the line.

y=mx+c

here c is the extra cost that is 6.50.

12m=10.80

For 12 bagels , the cost is 10.80, then the slope will be the cost of each bagel.

m=10.80/12

m=0.90

m=$0.90

Therefore, option c 0.90 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.

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Answer:

For b, you just start at (0,-5)(go down 5 on the y-axis), and go one up, one over to the right, and for c, just start at (0,0) and go right one, up 2

Step-by-step explanation:

The length of AC is 2.96 units using trigonometric ratio.

What are the trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

Given that angle A = 65° and AB = 7 units.

The base of △ABC is AC, height is BC, and hypotenuses is AB.

Cosine of angle is the ratio of base to hypotenuses.

Thus cos  65° = AC/AB

Substitute AB = 7

cos  65° = AC/7

Multiply both sides by 7:

7 × cos  65° = AC

Putting cos  65° = 0.42261826174

7 × 0.42261826174 =AC

AC = 2.95832783218

AC = 2.96 (nearest hundredth)

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Answer: D.

Hope it helps

To get (f-g)(x), we're essentially just factoring out x from f(x) and g(x).

-> f(x) - g(x) = x(f-g), and by the properties , x(f-g) is the same as (f-g)(x).

Therefore, (f-g)(x) = 5x - 7 - (-4x + 2) = 5x - 7 + 4x - 2 = 9x - 9.

Answer:

[tex](f-g)(x)=9x - 9[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x) = 5x-7 \\ g(x) = -4x + 2\end{cases}[/tex]

To find (f - g)(x), subtract function g(x) from function f(x):

[tex]\begin{aligned}(f-g)(x)&=f(x)-g(x)\\&=(5x-7)-(-4x+2)\\&=5x-7+4x-2\\&=5x+4x-7-2\\&=9x-9\end{aligned}[/tex]

Therefore, the solution to the given composite function is:

The translation rule is (x, y) ---> (x+8)(x-4).

What is translation rule?

A translation is a type of transformation that moves each point in a figure the same distance in the same direction. The second notation is a mapping rule of the form (x,y) → (x−7,y+5).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other.

Given,

let A =(x, y) ----> (x+9,y-2) and B =(x, y) ----> (x-1,y-2)

which means A is translated 9 units right and 2 units down

and B is translated 1 unit left and 2 units down.

Therefore, rule for composition is A+B

= (x, y) ------> (x+9-1, y-2-2)

(x,y) -----> (x+8,y-4)

which means translation is 8 units right and 4 units down.

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To simplify

First of all, Octavia error can be spotted from the correct steps below

Step1: Expand the expression

Step2: Collect like terms

Step 3: Simplify by using exponents laws

Step 4: Combine the terms.

The value is

Her error was that she didn't apply the exponents' law properly.

One of the laws she violated was

Her mistake was that she did

So she missed it from our step 1 above

From the graph given, we are asked to find the equation of line, with our answer in point slope form.

from the graph:

y = 9, x = 10

y1 = 5, x1 = 6

recall, the equation of a line is:

y = mx + b

slope m = y - y1/x - x1

m = 9 - 5/10 - 6

m = 4/4

m = 1

y = 1x + b

y = x + b

using the point slope form:

y - y1 = m(x - x1)

Where:

y = y coordinate of second point

y1 = y coordinate of point one

m = slope

x = x coordinate of second point

x2 = x coordinate of point one.

Therefore, the point slope equation is:

y - 5 = 1(x - 6)

y - 5 = x - 6

The price charge is $235 and the maximum revenue is $165675.

It is a plane curve that is mirror-symmetrical. It is approximately U-shaped. It is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. It is the locus of a fixed point that moves on a plane. It has many important applications. In Mathematics, the parabola plays a crucial role.

Number of members in club = 360

Monthly membership is of $350

For $ 1 price decrease and 3 people joinining

Membership charge will be = 350-x

Members will be 360+3x

Revenue equation will be

R (x) (350-1x)(360+3x)=0

126,000-360x+1050x-3x² =0

126,000+690x- 3x²-=0

This is a parabolic equation. Maximize the function to get

Differentiate to get the parabola vertex

R'(x) = 690-6x

So, 690-6x =0

x =115

Therefore, the price charge is

350-115 = $235

The number of members is

3360+115 = 705

The maximum revenue is given as

$235 × 705=$165675

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The GPA of a student who studies for 15 hours a week is 2.935.

What is a GPA?

Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.

How to calculate GPA?

To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.

Here,

We have an equation y = 0.164x + 0.475

put x= 15

we get,

y = 0.164* 15 + 0.475

y = 2.935

Hence, The GPA of a student who studies for 15 hours a week is 2.935

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Answer:

4 people will be on the last chair.

Step-by-step explanation:

60 divided by 5 is 12. There will be 12 full seats. 64 - 60 is 4 so there will be 4 more on the last chair.  

Hope this helped!

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-4)}) \implies y +8= 4 (x +4) \\\\\\ y+8=4x+16\implies {\Large \begin{array}{llll} y=4x+8 \end{array}}[/tex]

The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;

⇒ y = - 500x + 5500

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table shows the linear relationship between the number of water bottles remaining and the number of hours since 5:00 P.M.

Now,

Find the linear equation for the given table as;

Take number of hours = x

And, Number of remaining bottles = y

So, Two points for the linear equation as;

⇒ (x, y) = (1, 5000) , (2, 4500)

Thus, The linear equation for the table is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 5000 = (4500 - 5000) / (2 - 1) (x - 1)

⇒ y - 5000 = - 500 (x - 1)

⇒ y - 5000 = - 500x + 500

⇒ y = - 500x + 500 + 5000

⇒ y = - 500x + 5500

Thus, The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;

⇒ y = - 500x + 5500

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To find the area of the whole figure, we can divide it into two rectangles, the smaller rectangle has dimensions of 5 inches by 8 inches.

The bigger rectangle has dimensions of 9 inches by 15 inches.

Then, we add

In linear equation, 10 feet and 8 inches will require 4.6 pints.

What are instances of linear equations?

For 10 feet and 8 inches,          

12 inches = 1 foot,

therefore 8 inches = 8/12 foot = 0.6 foot

10 feet 8 inches = 10 + 0.6 = 10.6 feet

6 feet 8 inches required 3 pints

1 foot would have required (3/6.8) pints

10.6 feet will then require   (3/6.8)*10.6 = 4.6 pints.

Therefore 10 feet and 8 inches will require 4.6 pints.

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